Skip to main content
SpringerLink
Log in
Book cover

Proceedings of the Second International Conference on Soft Computing for Problem Solving (SocProS 2012), December 28-30, 2012 pp 199–207Cite as

On \(\alpha \)-Convex Multivalent Functions Defined by Generalized Ruscheweyh Derivatives Involving Fractional Differential Operator

  • Conference paper
  • First Online:

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 236))

Abstract

In the present investigation, we introduce a class of \(\alpha \)-convex multivalent functions defined by generalized Ruscheweyh derivatives introduced by Goyal and Goyal (J. Indian Acad. Math. 27(2):439–456, 2005) which involves a generalized fractional differential operator. The necessary and sufficient condition for functions to belong to this class is obtained. We study properties of this class and derive a theorem about image of a function from this class through generalized Komatu integral operator. Also, the integral representation for the functions of this class has been obtained.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   259.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Acu, M., et al.: On some \(\alpha \)-convex functions. Int. J. Open Problems Comput. Sci. Math 1(1), 1–10 (2008).

    Google Scholar 

  2. Ali, R.M., Ravichandran, V.: Classes of meromorphic \(\alpha \)-convex functions. Taiwanese J. Math. 14(4), 1479–1490 (2010)

    MATH  MathSciNet  Google Scholar 

  3. Duren, P.L.: Univalent funct. Springer Verlag, New York (1983)

    Google Scholar 

  4. Eenigenburg, P.J., Miller, S.S., Mocanu, P.T., Reade, M.O.: On a Briot-Bouquet differential subordination. General inequalities, 3. Int. Series of Numerical Math, pp. 339–348. Birkhauser Verlag, Basel (1983).

    Google Scholar 

  5. Goyal, S.P., Goyal, R.: On a class of multivalent functions defined by generalized Ruscheweyh derivatives involving a general fractional derivative operator. J. Indian Acad. Math. 27(2), 439–456 (2005)

    Google Scholar 

  6. Komatu, Y.: On analytic prolongation of a family of operators. Mathematica (Cluj) 32(55), 141–145 (1990)

    MathSciNet  Google Scholar 

  7. Ma, W., Minda, D.: A unified treatment of some special classes of univalent functions, proceedings of the conference on complex analysis, Tianjin, China. Int. Press. Conf. Proc. Lect. Notes Anal. 1, 157–169 (1994).

    Google Scholar 

  8. Miller, S.S., Mocanu, P.T.: On some classes of first-order differential subordinations. Michig. Math. J. 32, 185–195 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  9. Mocanu, P.T.: Une propriete de convexite geneealisee dans la theorie de la representation conforme. Mathematica (Cluj) 11(34), 127–133 (1969)

    MathSciNet  Google Scholar 

  10. Parihar, H.S., Agarwal, R.: Application of generalized Ruscheweyh derivatives on p-valent functions. J. Math. Appl. 34, 75–86 (2011)

    MathSciNet  Google Scholar 

  11. Raducanu, D., Nechita, V.O.: On \(\alpha \)-convex functions defined by generalized Ruscheweyh derivatives operator, Studia Univ. "Babes-Bolyai". Mathematica 53, 109–118 (2008)

    MATH  MathSciNet  Google Scholar 

  12. Ravichandran, V., Darus, M.: On class of \(\alpha \)-convex functions. J. Anal. Appl. 2(1), 17–25 (2004)

    MATH  MathSciNet  Google Scholar 

  13. Ravichandran, V., Seenivasagan, N., Srivastava, H.M.: Some inequalities associated with a linear operator defined for a class of multivalent functions. J. Inequal. Pure and Appl. Math. 4(4), 1–7 (2003). Art. 70.

    Google Scholar 

  14. Ruscheweyh, S.T.: New criterion for univalent functions. Proc. Amer. Math. Soc. 49, 109–115 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  15. Sokol, J.: On a condition for alpha-starlikeness. J. Math. Anal. Appl. 352, 696–701 (2009)

    Google Scholar 

  16. Srivastava, H.M., Saxena, R.K.: Operators of fractional integration and their applications. Appl. Math. Comput. 118, 1–52 (2001)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Malaviya National Institute of Technology, Jaipur, Rajasthan, India

    Ritu Agarwal

  2. Institute of Mathematics, University of Rzeszów, ul. Rejtana 16A, 35-310   , Rzeszów, Poland

    J. Sokol

Authors
  1. Ritu Agarwal
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Sokol
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ritu Agarwal .

Editor information

Editors and Affiliations

  1. Institute of Engineering and Technology, JK Lakshmipat University, Jaipur, Rajasthan, India

    B. V. Babu

  2. Department of Computer Science, Liverpool Hope University, Liverpool, United Kingdom

    Atulya Nagar

  3. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

    Kusum Deep

  4. Department of Paper Technology, Indian Institute of Technology Roorkee, Roorkee, India

    Millie Pant

  5. Department of Applied Mathematics, South Asian University, New Delhi, India

    Jagdish Chand Bansal

  6. Institute of Engineering and Technology, JK Lakshmipat University, Jaipur, Rajasthan, India

    Kanad Ray

  7. Institute of Engineering and Technology, JK Lakshmipat University, Jaipur, Rajasthan, India

    Umesh Gupta

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer India

About this paper

Cite this paper

Agarwal, R., Sokol, J. (2014). On \(\alpha \)-Convex Multivalent Functions Defined by Generalized Ruscheweyh Derivatives Involving Fractional Differential Operator. In: Babu, B., et al. Proceedings of the Second International Conference on Soft Computing for Problem Solving (SocProS 2012), December 28-30, 2012. Advances in Intelligent Systems and Computing, vol 236. Springer, New Delhi. https://doi.org/10.1007/978-81-322-1602-5_22

Download citation

  • DOI: https://doi.org/10.1007/978-81-322-1602-5_22

  • Published:

  • Publisher Name: Springer, New Delhi

  • Print ISBN: 978-81-322-1601-8

  • Online ISBN: 978-81-322-1602-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation